hw10.pdf - MODERN ALGEBRA 1 HOMEWORK 10(1 Chapter 7 2.5(2...

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MODERN ALGEBRA 1: HOMEWORK 10 (1) Chapter 7, 2.5 (2) Chapter 7, 2.9 (a), (b). (3) Chapter 7, 2.14 (4) Show that Aut ( Z / n Z ) = ( Z / n Z ) × . (5) Let p be a prime. Show that a group order p 2 is either isomorphic to Z p 2 or Z p × Z p . (Recall that we know it must be abelian.) (6) Show that there are at least two (non-isomorphic) groups of order 21. (7) We have a
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